(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schrödinger equation. The key idea is to rewrite the equation as an infinite-dimensional Hamiltonian system and discrete the system by using Fourier pseudospectral method in space and symplectic Euler method in time. After composing two different symplectic Euler methods for the ODEs resulted from semi-discretization in space, we get a new explicit scheme for the target equation which is of second order in space and spectral accuracy in time. The canonical Hamiltonian form of the resulted ODEs is presented and the new derived scheme is proved strictly to be symplectic. The new scheme is totally explicit whereas symplectic scheme is generally implicit or semi-implicit. Linear stability analysis is carried out and a necessary Courant-Friedrichs-Lewy condition is given. The numerical results are reported to test the accuracy and efficiency of the proposed method in long-term computing.